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Amino acid substitution models are a key component in phylogenetic analyses of protein sequences. All commonly used amino acid models available to date are time-reversible, an assumption designed for computational convenience but not for biological reality. Another significant downside to time-reversible models is that they do not allow inference of rooted trees without outgroups. In this article, we introduce a maximum likelihood approach nQMaker, an extension of the recently published QMaker method, that allows the estimation of time nonreversible amino acid substitution models and rooted phylogenetic trees from a set of protein sequence alignments. We show that the nonreversible models estimated with nQMaker are a much better fit to empirical alignments than pre-existing reversible models, across a wide range of data sets including mammals, birds, plants, fungi, and other taxa, and that the improvements in model fit scale with the size of the data set. Notably, for the recently published plant and bird trees, these nonreversible models correctly recovered the commonly estimated root placements with very high-statistical support without the need to use an outgroup. We provide nQMaker as an easy-to-use feature in the IQ-TREE software (http://www.iqtree.org), allowing users to estimate nonreversible models and rooted phylogenies from their own protein data sets. The data sets and scripts used in this article are available at https://doi.org/10.5061/dryad.3tx95x6hx. [amino acid sequence analyses; amino acid substitution models; maximum likelihood model estimation; nonreversible models; phylogenetic inference; reversible models.]

Using time-reversible Markov models is a very common practice in phylogenetic analysis, because although we expect many of their assumptions to be violated by empirical data, they provide high computational efficiency. However, these models lack the ability to infer the root placement of the estimated phylogeny. In order to compensate for the inability of these models to root the tree, many researchers use external information such as using outgroup taxa or additional assumptions such as molecular-clocks. In this study, we investigate the utility of non-reversible models to root empirical phylogenies and introduce a new bootstrap measure, the rootstrap, which provides information on the statistical support for any given root position.Availability and implementationrootstrap support is implemented in IQ-TREE 2 and a tutorial is available at the iqtree webpage http://www.iqtree.org/doc/Rootstrap. In addition, a python script is available at https://github.com/suhanaser/Rootstrap. [phylogenetic inference, root estimation, bootstrap, non-reversible models]

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Molecular sequence data that have evolved under the influence of heterotachous evolutionary processes are known to mislead phylogenetic inference. We introduce the General Heterogeneous evolution On a Single Topology (GHOST) model of sequence evolution, implemented under a maximum-likelihood framework in the phylogenetic program IQ-TREE (http://www.iqtree.org). Simulations show that using the GHOST model, IQ-TREE can accurately recover the tree topology, branch lengths, and substitution model parameters from heterotachously evolved sequences. We investigate the performance of the GHOST model on empirical data by sampling phylogenomic alignments of varying lengths from a plastome alignment. We then carry out inference under the GHOST model on a phylogenomic data set composed of 248 genes from 16 taxa, where we find the GHOST model concurs with the currently accepted view, placing turtles as a sister lineage of archosaurs, in contrast to results obtained using traditional variable rates-across-sites models. Finally, we apply the model to a data set composed of a sodium channel gene of 11 fish taxa, finding that the GHOST model is able to elucidate a subtle component of the historical signal, linked to the previously established convergent evolution of the electric organ in two geographically distinct lineages of electric fish. We compare inference under the GHOST model to partitioning by codon position and show that, owing to the minimization of model constraints, the GHOST model offers unique biological insights when applied to empirical data.

Proteins have distinct structural and functional constraints at different sites that lead to site-specific preferences for particular amino acid residues as the sequences evolve. Heterogeneity in the amino acid substitution process between sites is not modeled by commonly used empirical amino acid exchange matrices. Such model misspecification can lead to artefacts in phylogenetic estimation such as long-branch attraction. Although sophisticated site-heterogeneous mixture models have been developed to address this problem in both Bayesian and maximum likelihood (ML) frameworks, their formidable computational time and memory usage severely limits their use in large phylogenomic analyses. Here we propose a posterior mean site frequency (PMSF) method as a rapid and efficient approximation to full empirical profile mixture models for ML analysis. The PMSF approach assigns a conditional mean amino acid frequency profile to each site calculated based on a mixture model fitted to the data using a preliminary guide tree. These PMSF profiles can then be used for in-depth tree-searching in place of the full mixture model. Compared with widely used empirical mixture models with $k$ classes, our implementation of PMSF in IQ-TREE (http://www.iqtree.org) speeds up the computation by approximately $k$/1.5-fold and requires a small fraction of the RAM. Furthermore, this speedup allows, for the first time, full nonparametric bootstrap analyses to be conducted under complex site-heterogeneous models on large concatenated data matrices. Our simulations and empirical data analyses demonstrate that PMSF can effectively ameliorate long-branch attraction artefacts. In some empirical and simulation settings PMSF provided more accurate estimates of phylogenies than the mixture models from which they derive.

[Abstract] We introduce the Phylogenetic Likelihood Library (PLL), a highly optimized application programming interface for developing likelihood-based phylogenetic inference and postanalysis software. The PLL implements appropriate data structures and functions that allow users to quickly implement common, error-prone, and labor-intensive tasks, such as likelihood calculations, model parameter as well as branch length optimization, and tree space exploration. The highly optimized and parallelized implementation of the phylogenetic likelihood function and a thorough documentation provide a framework for rapid development of scalable parallel phylogenetic software. By example of two likelihood-based phylogenetic codes we show that the PLL improves the sequential performance of current software by a factor of 2–10 while requiring only 1 month of programming time for integration. We show that, when numerical scaling for preventing floating point underflow is enabled, the double precision likelihood calculations in the PLL are up to 1.9 times faster than those in BEAGLE. On an empirical DNA dataset with 2000 taxa the AVX version of PLL is 4 times faster than BEAGLE (scaling enabled and required). DFG, German Research Foundation; STA/860-4. F.I.-C. DFG, German Research Foundation; STA/860-3 DFG, German Research Foundation; STA/860-2. L.-T.N. University of Vienna; I059-N Austrian Science Fund; I760-B17

The "phylogenetic diversity" (PD) measure of biodiversity is evaluated using a phylogenetic tree, usually inferred from morphological or molecular data. Consequently, it is vulnerable to errors in that tree, including those resulting from sampling error, model misspecification, or conflicting signals. To improve the robustness of PD, we can evaluate the measure using either a collection (or distribution) of trees or a phylogenetic network. Recently, it has been shown that these 2 approaches are equivalent but that the problem of maximizing PD in the general concept is NP-hard. In this study, we provide an efficient dynamic programming algorithm for maximizing PD when splits in the trees or network form a circular split system. We illustrate our method using a case study of game birds ("Galliformes") and discuss the different choices of taxa based on our approach and PD.

We consider a (phylogenetic) tree with n labeled leaves, the taxa, and a length for each branch in the tree. For any subset of k taxa, the phylogenetic diversity is defined as the sum of the branch-lengths of the minimal subtree connecting the taxa in the subset. We introduce two time-efficient algorithms (greedy and pruning) to com- pute a subset of size k with maximal phylogenetic diversity in O(«log/c) and O(n + (n - k) login - k)) time, respec- tively. The greedy algorithm is an efficient implementation of the so-called greedy strategy (Steel, 2005; Pardi and Goldman, 2005), whereas the pruning algorithm provides an alternative description of the same problem. Both algo- rithms compute within seconds a subtree with maximal phylogenetic diversity for trees with 100,000 taxa or more. (Biodiversity conservation; Comparative genomics; Greedy algorithm; Phylogenetic diversity; Phylogenetic tree; Pruning algorithm.)